One mole of an ideal gas undergoes a process P=(P0/1+(V0 / V)2) . Here P0 and V0 are constants. The change in temperature of the gas when volume is changed from V=V0 to V=2 V0 is (x P0 V0/10 R) . Find x. (Here R= Universal gas constant)

Question

One mole of an ideal gas undergoes a process P=(P0/1+(V0 / V)2) . Here P0 and V0 are constants. The change in temperature of the gas when volume is changed from V=V0 to V=2 V0 is (x P0 V0/10 R) . Find x. (Here R= Universal gas constant) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

P V=n R T At V=V0: R T1=((P0/2))(V0) At V=2 V0: R T2=((4 P0/5))(2 V0) ⇒ T2-T1=(11 P0 V0/10 R)

Q. One mole of an ideal gas undergoes a process P=1+(V0​/V)2P0​​. Here P0​ and V0​ are constants. The change in temperature of the gas when volume is changed from V=V0​ to V=2V0​ is 10RxP0​V0​​. Find x. (Here R= Universal gas constant)

PV=nRT At V=V0​:RT1​=(2P0​​)(V0​) At V=2V0​:RT2​=(54P0​​)(2V0​) ⇒T2​−T1​=10R11P0​V0​​

$P V = n RT$
At $V = V_{0} : R T_{1} = (\frac{P _{0}}{2}) (V_{0})$
At $V = 2 V_{0} : R T_{2} = (\frac{4 P _{0}}{5}) (2 V_{0})$
$\Rightarrow T_{2} - T_{1} = \frac{11 P _{0} V _{0}}{10 R}$