Thermodynamics

Question

One mole of a monoatomic ideal gas undergoes the process A → B in the given p-V diagram. The molar heat capacity for this process is

$\frac{3 R}{2}$

$\frac{13 R}{6}$

$\frac{5 R}{2}$

2R

Solution

$\frac{13 R}{6}$

A pressure-volume ( or PV diagram or volume-pressure loop) is used to describe corresponding changes in volume and pressure in a system. They are commonly used in thermodynamics, cardiovascular physiology, and respiratory physiology.

$W_{A \to B} =$ Area under p-V diagram

= 4 V₀ × 3 $p_{0} + \frac{1}{2} 4 V_{0} \times 3 p_{0}$

= 18 p₀ V₀

∴ ΔU = nC_v ΔT

= 1. $\frac{3}{2} R (T_{B} - T_{A})$

= $\frac{3}{2} R (\frac{30 p_{0} V_{0}}{R} - \frac{3 p_{0} V_{0}}{R})$

= $\frac{81}{2} p_{0} V_{0}$

Thus, $∆ Q_{A \to B} = ∆ W_{A \to B} + ∆ U_{A \to B}$

= 18 $p_{0} V_{0} + \frac{81}{2} p_{0} V_{0}$

$∆ Q_{A \to B}$ = $\frac{117}{2} p_{0} V_{0}$

Molar heat capacity

C = $\frac{∆ Q}{n ∆ T}$

= $\frac{117 p_{0} \frac{V_{0}}{2}}{\frac{30 p_{0} V_{0}}{R} - \frac{3 p_{0} V_{0}}{R}}$

= $\frac{117 p_{0} \frac{V_{0}}{2}}{\frac{27 p_{0} V_{0}}{R}}$

C = $\frac{13 R}{6}$

Some More Questions From Thermodynamics Chapter

A system goes from A to B via two processes I and II as shown in the figure. If ∆U₁ and ∆U₂ are the changes in internal energies in the processes I and II respectively, the

Which of the following statements is correct for any thermodynamic system?

Thermodynamic processes are indicated in the following diagram.

Match the following

Column-1 Column-2
P. Process I a. Adiabatic
Q. Process II b. Isobaric
R. Process III c. Isochoric
S. Process IV d. Isothermal

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Thermodynamics

One mole of a monoatomic ideal gas undergoes the process A → B in the given p-V diagram. The molar heat capacity for this process is

$\frac{3 R}{2}$

$\frac{13 R}{6}$

$\frac{5 R}{2}$

2R

Some More Questions From Thermodynamics Chapter

A system goes from A to B via two processes I and II as shown in the figure. If ∆U₁ and ∆U₂ are the changes in internal energies in the processes I and II respectively, the

Which of the following statements is correct for any thermodynamic system?

Thermodynamic processes are indicated in the following diagram.

Match the following

Column-1 Column-2
P. Process I a. Adiabatic
Q. Process II b. Isobaric
R. Process III c. Isochoric
S. Process IV d. Isothermal

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Loaction

Column-1	Column-2
P. Process I	a. Adiabatic
Q. Process II	b. Isobaric
R. Process III	c. Isochoric
S. Process IV	d. Isothermal

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Thermodynamics

One mole of a monoatomic ideal gas undergoes the process A → B in the given p-V diagram. The molar heat capacity for this process is 3R2 13 R6 5 R2 2R

Some More Questions From Thermodynamics Chapter

A system goes from A to B via two processes I and II as shown in the figure. If ∆U1 and ∆U2 are the changes in internal energies in the processes I and II respectively, the

Which of the following statements is correct for any thermodynamic system?

Thermodynamic processes are indicated in the following diagram.Match the following Column-1 Column-2 P. Process I a. Adiabatic Q. Process II b. Isobaric R. Process III c. Isochoric S. Process IV d. Isothermal

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

One mole of a monoatomic ideal gas undergoes the process A → B in the given p-V diagram. The molar heat capacity for this process is

$\frac{3 R}{2}$

$\frac{13 R}{6}$

$\frac{5 R}{2}$

2R

A system goes from A to B via two processes I and II as shown in the figure. If ∆U₁ and ∆U₂ are the changes in internal energies in the processes I and II respectively, the

Thermodynamic processes are indicated in the following diagram.

Match the following

Column-1 Column-2
P. Process I a. Adiabatic
Q. Process II b. Isobaric
R. Process III c. Isochoric
S. Process IV d. Isothermal