Calculations specific heat capacity

Figure 36 Calculated specific heat capacity of various polyolefins at constant volume as a function of temperature. (From Ref 32.)...

The specific heat capacity of humid air calculated per kilogram of dry air is... 

We can calculate the heat capacity of a substance from its mass and its specific heat capacity by using the relation C = m X Cs. If we know the mass of a substance, its specific heat capacity, and the temperature rise it undergoes during an experiment, then the heat supplied to the sample is... 

These expressions may be rearranged to calculate the specific or molar heat capacity from the measured temperature rise caused by a known quantity of heat. The specific heat capacity of a dilute solution is normally taken to be the same as that of the pure solvent (which is commonly water). Table 6.2 lists the specific and molar heat capacities of sume common substances. 

Sf.I.F-Tfst 6.3A Potassium perchlorate, KC104, is used as an oxidizer in fireworks. Calculate the heat required to raise the temperature of 10.0 g of KCIO4 from 25°C to an ignition temperature of 900.°C. The specific heat capacity of KC1C4 is 0.8111... 

This program can be used to calculate the heat input or cooling required for a process unit, where the stream enthalpies relative to the datum temperature can be calculated from the specific heat capacities of the components (equation 3.11). 

Calculate the specific enthalpy of water at a pressure of 1 bar and temperature of 200 °C. Check your value using steam tables. The specific heat capacity of water can be calculated from the equation ... 

Assuming plug flow of the gas and complete mixing of the solids, calculate the coefficient for heat transfer between the particles and the gas. The specific heat capacity of air is 0.85 kJ/kg K. 

A single-effect evaporator is used to concentrate 7 kg/s of a solution from 10 to 50 per cent of solids. Steam is available at 205 kN/m2 and evaporation takes place at 13.5 kN/m2. If the overall heat transfer coefficient is 3 kW/m2 K, calculate the heating surface required and the amount of steam used if the feed to the evaporator is at 294 K and the condensate leaves the heating space at 352.7 K. The specific heat capacity of a 10 per cent solution is 3.76 kJ/kgK, the specific heat capacity of a 50 per cent solution is 3.14 kJ/kgK. 

Distilled water is produced from sea water by evaporation in a single-effect evaporator working on the vapour compression system. The vapour produced is compressed by a mechanical compressor of 50 per cent efficiency, and then returned to the calandria of the evaporator. Extra steam, dry and saturated at 650 kN/m2, is bled into the steam space through a throttling valve. The distilled water is withdrawn as condensate from the steam space. 50 per cent of the sea water is evaporated in the plant. The energy supplied in addition to that necessary to compress the vapour may be assumed to appear as superheat in the vapour. Calculate the quantity of extra steam required in kg/s. The production rate of distillate is 0.125 kg/s, the pressure in the vapour space is 101.3 kN/m2, the temperature difference from steam to liquor is 8 deg K, the boiling-point rise of sea water is 1.1 deg K and the specific heat capacity of sea water is 4.18 kJ/kgK. 

For the purpose of calculation, it may be assumed that the specific heat capacity is 4.18 kJ/kgK, that there is no boiling point rise, and that the latent heat of vaporisation is constant at 2330 kJ/kg over the temperature range in the system. The overall heat transfer coefficients may be taken as 2.5, 2.0 and 1.6 kW/m2 K in the first, second and third effects, respectively. 

A single-effect evaporator with a heating surface area of 10 m2 is used to concentrate a NaOH solution flowing at 0.38 kg/s from 10 per cent to 33.3 per cent. The feed enters at 338 K and its specific heat capacity is 3.2 kJ/kg K. The pressure in the vapour space is 13.5 kN/m2 and 0.3 kg/s of steam is used from a supply at 375 K. Calculate ... 

Nitrogen contained in a large tank at a pressure P = 200000 Pa and a temperature of 300 K flows steadily under adiabatic conditions into a second tank through a converging nozzle with a throat diameter of 15 mm. The pressure in the second tank and at the throat of the nozzle is P, = 140000 Pa. Calculate the mass flow rate, M, of nitrogen assuming frictionless flow and ideal gas behaviour. Also calculate the gas speed at the nozzle and establish that the flow is subsonic. The relative molecular mass of nitrogen is 28.02 and the ratio of the specific heat capacities y is 1.39. 

The specific heat capacity commonly has units of J/g-K. Because of the original definition of the calorie, the specific heat capacity of water is 4.184 J/g-K. If the specific heat capacity, the mass, and the change of temperature are all known, the amount of energy absorbed can easily be calculated. 

You can use the specific heat capacity of a substance to calculate the amount of energy that is needed to heat a given mass a certain number of degrees. You can also use the specific heat capacity to determine the amount of heat that is released when the temperature of a given mass decreases. The specific heat capacity of liquid water, as shown in Table 5.2, is 4.184 J/g °C. This relatively large value indicates that a considerable amount of energy is needed to raise or lower the temperature of water. 

You can use the following equation to calculate the heat change of a substance, based on the mass of the substance. You can also use this equation to calculate the specific heat capacity of the substance and the change in its temperature. 

Step 2 Use the equation Q = m c AT to calculate the amount of heat that is absorbed by the solution (in J). Assume that the reaction mixture has the same specific heat capacity as water (c= 4.184 J/g.°C). 

The chemist uses a coffee-cup calorimeter to neutralize completely 61.1 mL of 0.543 mol/L HCl(aq) with 42.6 mL of NaOH(aq). The initial temperature of both solutions is 17.8°C. After neutralization, the highest recorded temperature is 21.6°C. Calculate the enthalpy of neutralization, in units of kJ/mol of HCl. Assume that the density of both solutions is 1.00 g/mL. Also assume that the specific heat capacity of both solutions is the same as the specific heat capacity of water. 

As an example of the use of the heat capacity values, calculate the calories required to heat 1 kilogram of aluminum from 10° C to 70° C. Multiply the grams of metal by the 60° C increase by the specific heat capacity ... 

Calorimetry is the measurement of heat changes that accompany a process (see Chapter 15 for details). The important values to know are heat (q), mass (m), specific heat capacity (C, and the change in temperature (AT). If you know any three of these values, you can calculate the fourth with this equation ... 

Be sure that your units of heat, mass, and temperature match those used in your specific heat capacity before attempting any calculations. 

Empirical equations are often used in engineering calculations. Eor example, the following type of equation can relate the specific heat capacity Cp (J kg K ) of a substance with its absolute temperature T (K). 

To determine the amount of heat absorbed by the glass of the calorimeter beaker, mark the level of the water in the beaker when running the experiment. Use the data obtained to approximately determine the mass of the glass heated by the water. Consider that the mass of the thermometer glass immersed in the liquid is about 2 g. Use the found specific heat capacity to calculate the atomic mass of lead by the Dulong and Petit law. 

The specific and molar heat capacities of some common substances are given in Table 6.1. Note that, although the values of the specific heat capacities are listed in joules per degree Celsius per gram (J-(°C) 1 -g 1), they could equally well be reported in joules per kelvin per gram (J-K 1-g ) with the same numerical values, because the size of the Celsius degree and the kelvin are the same. We can calculate the heat capacity of a substance from its mass and its specific heat capacity by rearranging the definition Cs = dm into C = mCs. Then we can use... 

Near room temperature, the specific heat capacity of benzene is 1.05 J-(°C) 1-g 1. Calculate the heat needed to raise the temperature of 50.0 g of benzene from 25.3°C to 37.2°C. (b) A 1.0-kg block of aluminum is supplied with 490 kj of heat. What is the temperature change of the aluminum The specific heat capacity of aluminum is 0.90 J-(°C) 1-g l. 

The specific heat capacity of stainless steel is 0.51 J-rCp-g . (a) Calculate the heat that must be supplied to a 500.0-g stainless steel vessel containing 450.0 g of water to raise its temperature from 25.0°C to the boiling point of water, 100.0°C. (b) What percentage of the heat is used to raise the temperature of the water (c) Compare these answers with those of Exercise 6.17. 

A piece of copper of mass 20.0 g at 100.0°C is placed in an insulated vessel of negligible heat capacity but containing 50.7 g of water at 22.0°C. Calculate the final temperature of the water. Assume that all the energy lost by the copper is gained by the water. The specific heat capacity of copper is 0.38 J-(°C) 1-g 1. 

Calculate the mass loss or gain for each of the following processes (a) a 50.0-g block of iron (specific heat capacity, 0.45 J-(°C)"1-g 1) cools from 600°C to... 

With additional information, including the heat capacity of the buffer solvent, the partial specific volumes (volume per gram of the solute), and the specific volume of the solvent, one can extract the partial specific heat capacity (J K 1g I) of the solute. Privalov has summarized these calculations.8 Because the solutions are studied at very low concentrations, it is assumed that the contribution to the total heat capacity from the solvent cancels out when one calculates the excess heat capacity. With only minor exceptions, the procedures used to calculate parameters associated with the transformations in nucleic acids and in proteins are the same and yield quantities that are interpreted in similar ways, although researchers in these two fields may use a different notation for the same quantity. 

By definition, the heat capacity of a system is the amount of energy required to raise its temperature by 1 K. The unit is J KT1. To allow calculations and comparisons, the specific heat capacity is more commonly used ... 

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