C_P is always greater than C_V for an ideal g | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For an ideal gas,the relationship between molar heat capacities is given by Mayer's relation: $C_P - C_V = R$. At constant volume,the work done by

Vedclass · Accepted Answer

No work is done by a gas at constant volume.

Vedclass · Answer

(B) For an ideal gas,the relationship between molar heat capacities is given by Mayer's relation: $C_P - C_V = R$. At constant volume,the work done by the gas is zero $(w = 0)$ because there is no change in volume $(dV = 0)$. Therefore,all the heat supplied at constant volume is used to increase the internal energy of the system $(q_V = \Delta U)$. At constant pressure,some heat is used to increase the internal energy and some is used to perform work of expansion $(q_P = \Delta U + P\Delta V)$. Since the internal energy change $(\Delta U)$ depends only on temperature for an ideal gas,it is the same for both processes for the same temperature change. Thus,$C_P$ must be greater than $C_V$ because additional heat is required to perform work at constant pressure.

$C_P$ is always greater than $C_V$ for an ideal gas. Choose the correct option.

Similar Questions

What is heat capacity?

The molar heat capacity of water at constant pressure is $75 \, J \, K^{-1} \, mol^{-1}$. When $1.0 \, kJ$ of heat is supplied to $100 \, g$ of water which is free to expand,the increase in temperature of water is (in $, K$)

Explain Heat Capacity.

What will be the $\Delta U$ value,when one mole of oxygen $(O_2)$ is heated from $-20^{\circ} C$ to $40^{\circ} C$ at constant volume (in $J$)? (Molar heat capacity for oxygen $\simeq 20.8 \ J \ mol^{-1} \ K^{-1}$)

Molar heat capacity $(C_p)$ of water at constant pressure is $75 \ J \ K^{-1} \ mol^{-1}$. The increase in temperature (in $K$) of $100 \ g$ of water when $1 \ kJ$ of heat is supplied to it is

Vedclass Test Series

Exam Paper Generator

Online Exam Module