Question 444: Thermodynamics & KTG

Question

One mole of ideal gas passes through a process where pressure and volume obey the relation
$$P = {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over V}} \right)}^2}} \right]$$.
Here P0 and V0 are constants. Calculate the change in the temperature of the gas if its
volume changes form V0 to 2V0

Accepted Answer

Given $$P = {P_o}\left\{ {1 - {1 \over 2}{{\left( {{{{V_o}} \over V}} ight)}^2}} ight\};$$ ...(i)
As n = 1 mole
$$ 	herefore $$ PV = nRT = RT
$$ \Rightarrow $$ P = $${{RT} \over V}$$ ....(ii)
From (i) and (ii), we get
$${{RT} \over V} = {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over V}} ight)}^2}} ight]$$
$$ \Rightarrow $$ T = $${V \over R} 	imes {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over V}} ight)}^2}} ight]$$
Case 1 : when V = V
0
then T
i
= $${{{V_0}} \over R} 	imes {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over {{V_0}}}} ight)}^2}} ight]$$
= $${{{V_0}{P_0}} \over {2R}}$$
Case 2 : when V = 2V
0
then T
f
= $${{2{V_0}} \over R} 	imes {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over {2{V_0}}}} ight)}^2}} ight]$$
= $${7 \over 4}{{{P_0}{V_0}} \over R}$$
Then $$\Delta $$T = T
f
- T
i
= $${7 \over 4}{{{P_0}{V_0}} \over R} - {{{P_0}{V_0}} \over {2R}}$$
= $${{{P_0}{V_0}} \over R}\left( {{7 \over 4} - {1 \over 2}} ight)$$
= $${5 \over 4}{{{P_0}{V_0}} \over R}$$

Answer

$${3 \over 4}{{{P_0}{V_0}} \over R}$$

Answer

$${1 \over 2}{{{P_0}{V_0}} \over R}$$

Answer

$${5 \over 4}{{{P_0}{V_0}} \over R}$$

Answer

$${1 \over 4}{{{P_0}{V_0}} \over R}$$

Thermodynamics & KTG

One mole of ideal gas passes through a process where pressure and volume obey the relation $P = {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over V}} \right)}^2}} \right]$. Here P0 and V0 are constants. Calculate the change in the temperature of the gas if its volume changes form V0 to 2V0

Choose the correct answer: