One mole of an ideal gas left( {frac{{{C_P}}}{{{C_V}}}, = gamma } right) heated by law P=alpha V where P is pressure of gas, V is

Q: One mole of an ideal gas $\left( {\frac{{{C_P}}}{{{C_V}}}\, = \gamma } \right)$ heated by law $P=\alpha V$ where $P$ is pressure of gas, $V$ is volume, $\alpha$ is a constant what is the heat capacity of gas in the process-

d $\mathrm{C}=\frac{\mathrm{Q}}{\mathrm{n} \Delta \mathrm{T}} \frac{\Delta U+W}{n \Delta T}=\frac{n C_{V} \Delta t+\int_{V_{i}}^{V_{f}} P d V}{n \Delta T}$ $=\mathrm{C}_{\mathrm{v}}+\frac{\alpha}{n \Delta t} \cdot \int_{V_{t}}^{v_{f}} V d V$ $=\frac{R}{\gamma-1}+\frac{1}{2} \frac{\alpha V_{f}^{2}-\alpha V_{i}^{2}}{n \Delta T}$ $=\frac{R}{\gamma-1}+\frac{1}{2} \frac{P_{f} V_{f}-P_{i} V_{i}}{n \Delta T}$ $=R\left[\frac{1}{\gamma-1}+\frac{1}{2}\right]=\frac{R}{2}\left(\frac{\gamma+1}{\gamma-1}\right)$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

One mole of an ideal gas $\left( {\frac{{{C_P}}}{{{C_V}}}\, = \gamma } \right)$ heated by law $P=\alpha V$ where $P$ is pressure of gas, $V$ is volume, $\alpha$ is a constant what is the heat capacity of gas in the process-

A$C\, = \,\frac{R}{{\gamma - 1}}$
B$C\, = \,\frac{{\gamma R}}{{\gamma - 1}}$
C$C\, = \,\frac{{R\left( {\gamma - 1} \right)}}{{2\left( {\gamma + 1} \right)}}$
D$C\, = \,\frac{{R\left( {\gamma + 1} \right)}}{{2\left( {\gamma - 1} \right)}}$

Advanced

STD 11 Science
JEE
STD 11 - 12 . kinetic theory of gases
Physics

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Download App

Download our appand get started for free

Similar Questions

Download our app
and get started for free