202k views
1 vote
Explain briefly why a gas has two specific heat capacities. 0.01 kg of a gas is heated from 23°C to 215°C. The specific heat capacity of the gas at constant volume is c = 0.72 kJ/kgK and the specific heat capacity at constant pressure Cp = 1.01 kJ/kgK. Calculate the change in a. Enthalpy b. Internal energy c. Flow energy

User Vyudi
by
8.3k points

1 Answer

1 vote

Final answer:

A gas has two specific heat capacities (Cv and Cp) because the heat required for a temperature increase varies depending on volume or pressure constancy. Enthalpy change is 1.9392 kJ, internal energy change is 1.3824 kJ, and flow energy change (if referring to work done at constant pressure) is 0.5568 kJ.

Step-by-step explanation:

A gas has two specific heat capacities because the amount of heat required to raise its temperature by one degree depends on whether its volume is held constant (constant volume, Cv) or if its pressure is held constant (constant pressure, Cp). Specific heat at constant volume doesn't account for any work done by the gas during expansion, whereas specific heat at constant pressure includes the energy used for work during expansion at constant pressure.

To calculate the change in enthalpy (ΔH), we use

ΔH = m*Cp*ΔT,

where m is the mass of the gas, Cp is the specific heat at constant pressure, and ΔT is the change in temperature. Since 0.01 kg of gas is heated from 23°C to 215°C, ΔT is 215°C - 23°C = 192 K.

The change in enthalpy is then ΔH = 0.01 kg * 1.01 kJ/kgK * 192 K, which equals 1.9392 kJ.

In terms of internal energy change (ΔU), we use

ΔU = m*Cv*ΔT.

Using the same ΔT and m, with Cv = 0.72 kJ/kgK, the change in internal energy is

ΔU = 0.01 kg * 0.72 kJ/kgK * 192 K, which equals 1.3824 kJ.

The flow energy change is not typically a term used in this context, but assuming it refers to the work done by the gas during expansion at constant pressure, we can derive it from the first law of thermodynamics.

Considering ΔH = ΔU + PΔV (where PΔV represents the work done by the gas), if the process is at constant pressure, PΔV is the difference between ΔH and

ΔU: 1.9392 kJ - 1.3824 kJ = 0.5568 kJ.

User MarcoS
by
7.7k points