Question

In a adiabatic change,the pressure and temperature of a monoatomic gas are related as P∞T^c.Here c equals: a)2/5 b)3/5 c)5/2 d)5/3.

Answer 1

Answer on Question #38031, Physics, Other

Question:

In a adiabatic change, the pressure and temperature of a monoatomic gas are related as $P \propto T^{\wedge}c$. Here $c$ equals:

a) 2/5

b) 3/5

c) 5/2

d) 5/3.

Answer:

The mathematical equation for an ideal gas undergoing a reversible (i.e., no entropy generation) adiabatic process is:

$$P V ^ {\gamma} = c o n s t$$

For a monatomic ideal gas, $\gamma = \frac{5}{3}$. Assuming $PV = RT$:

$$P ^ {1 - \gamma} T ^ {\gamma} = c o n s t$$

or

$$P \propto T ^ {- \frac {\gamma}{1 - \gamma}} = T ^ {\frac {5}{3} \frac {3}{2}} = T ^ {\frac {5}{2}}$$

Answer: c) 5/2