One mole of an ideal gas has internal energy given by U=U0+2PV , where P is the pressure and V is the volume of the gas. U0 is a constant. This gas undergoes the quasi-static cyclic process ABCD as shown in the U-V diagram The molar heat capacity of the gas at constant pressure is

Question

One mole of an ideal gas has internal energy given by U=U0+2PV , where P is the pressure and V is the volume of the gas. U0 is a constant. This gas undergoes the quasi-static cyclic process ABCD as shown in the U-V diagram <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-pusfukyzzyd28zzc.jpg" /> The molar heat capacity of the gas at constant pressure is (A) 2R (B) 3R (C) (5/2)R (D) 4R

Tardigrade Admin · Accepted Answer

Given relation for internal energy is U=U0+2PV . For this cyclic process change in internal energy is given by Δ U=2Δ (P V)=2RΔ T ⇒ CV=2R ⇒ Cp=CV+R=3R

$2 R$

$3 R$

$\frac{5}{2} R$

$4 R$

Given relation for internal energy is $U = U_{0} + 2 P V$ .
For this cyclic process change in internal energy is given by
$Δ U = 2Δ (P V) = 2 R Δ T$
$\Rightarrow C_{V} = 2 R$
$\Rightarrow C_{p} = C_{V} + R = 3 R$

Q. One mole of an ideal gas has internal energy given by U=U0​+2PV , where P is the pressure and V is the volume of the gas. U0​ is a constant. This gas undergoes the quasi-static cyclic process ABCD as shown in the U−V diagram The molar heat capacity of the gas at constant pressure is

2R

3R

25​R

4R

Given relation for internal energy is U=U0​+2PV . For this cyclic process change in internal energy is given by ΔU=2Δ(PV)=2RΔT ⇒CV​=2R ⇒Cp​=CV​+R=3R

$2 R$

$3 R$

$\frac{5}{2} R$

$4 R$

Given relation for internal energy is $U = U_{0} + 2 P V$ .
For this cyclic process change in internal energy is given by
$Δ U = 2Δ (P V) = 2 R Δ T$
$\Rightarrow C_{V} = 2 R$
$\Rightarrow C_{p} = C_{V} + R = 3 R$