Which of the following statements is correct?

{(\frac{\partial H}{\partial T})}_{p} - {(\frac{\partial U}{\partial T})}_{v} = R

No worries! We‘ve got your back. Try BYJU‘S free classes today!

{(\frac{\partial H}{\partial T})}_{p} > {(\frac{\partial U}{\partial T})}_{v}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

{(\frac{\partial U}{\partial V})}_{T}

for ideal gas is zero

No worries! We‘ve got your back. Try BYJU‘S free classes today!

All of the above

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D All of the above
The difference between the molar heat capacities at constant pressure and constant volume is equal to the ideal gas constant R.
Hence, $(C_{p} - C_{v}) = R$
But, $C_{p} = {(\frac{\partial H}{\partial T})}_{P}$ and $C_{v} = {(\frac{\partial U}{\partial T})}_{V}$
Hence, ${(\frac{\partial H}{\partial T})}_{p} - {(\frac{\partial U}{\partial T})}_{v} = R$
The molar heat capacity at constant pressure is greater than the molar heat capacity at constant volume as can be seen from the previous relationship as the R value is positive.

During an isothermal process, the temperature remains constant. Hence, the internal energy of the system remains constant. Thus, for an ideal gas, the term ${(\frac{\partial U}{\partial V})}_{T}$ is equal to zero.

Suggest Corrections

Similar questions

Which of the following statements is correct for the reaction $C O (g) + \frac{1}{2} O_{2} (g) \to C O_{2} (g)$ at constant temperature and pressure?

Q. The first law of thermodynamics can be written as

Δ U

= q +w for an ideal gas. Which of the following statements is correct?

What are the values of $Δ U$ and $Δ H$ when $10 d m^{3}$ of Helium at NTP is heated in a cylinder to $100^{\circ} C$ , assuming that the gas behaves ideally. ( $C_{V} = \frac{3}{2} R$ )

Q. For which of the following reaction

△ H \neq △ U

Q. Consider the following statements:
(a) Molecular mass of

C H_{3} O H

32 u .

(b) In

N H_{3}

, the ratio of

N

and

H

by mass is

14 : 3.

C a C l_{2}

111 u .

(d) Isotopes have same mass number.

Which of the above statements are correct?

Join BYJU'S Learning Program