Prove that cp is greater than cv.

1.	Prove that cp is greater than cv.
Answer» Out of the two specific heats of a gas, C_{p >}C_v This can be understood as follows: In case C_v volume of the gas is kept constant and heat is required only for raising the temperature of gas through 1°C or 1K. No heat whatsoever is spent in expansion of the gas. In case of C_P as pressure of the gas is kept constant and the gas could expand on heating. ∴ Some heat is spent in expansion of the gas against external pressure. Hence, more heat is required to raise the temperature of 1 gm mole of the gas through 1°C or 1K when heated at constant pressure. Hence, C_{p >}C_v .

Answer»

Out of the two specific heats of a gas,

C_{p >}C_v

This can be understood as follows:

In case C_v volume of the gas is kept constant and heat is required only for raising the temperature of gas through 1°C or 1K. No heat whatsoever is spent in expansion of the gas.

In case of C_P as pressure of the gas is kept constant and the gas could expand on heating.

∴ Some heat is spent in expansion of the gas against external pressure.

Hence, more heat is required to raise the temperature of 1 gm mole of the gas through 1°C or 1K when heated at constant pressure. Hence, C_{p >}C_v .

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