A gas at temperature 27° C and pressure 30 atm. is allowed to expand to 1 atm pressure. If the volume becomes 10 times its initial volume, the final temperature becomes:

Question

A gas at temperature 27° C and pressure 30 atm. is allowed to expand to 1 atm pressure. If the volume becomes 10 times its initial volume, the final temperature becomes: (A)  100° C  (B) 373 K (C)  373° C  (D)  -173° C

Tardigrade Admin · Accepted Answer

Ideal gas equation is PV=RT⇒ PV propto T Hence, (P1V1/T1)=(P2V2/T2) (30V/300)=(1× 10V/T2) T2=(300× 10/30)=100K=-173 oC

Q. A gas at temperature $27^{\circ} C$ and pressure 30 atm. is allowed to expand to 1 atm pressure. If the volume becomes 10 times its initial volume, the final temperature becomes:

$100^{\circ} C$

373 K

$373^{\circ} C$

$- 173^{\circ} C$

Ideal gas equation is $P V = RT \Rightarrow P V \propto T$ Hence, $\frac{P _{1} V _{1}}{T _{1}} = \frac{P _{2} V _{2}}{T _{2}}$ $\frac{30 V}{300} = \frac{1 \times 10 V}{T _{2}}$ $T_{2} = \frac{300 \times 10}{30} = 100 K = - 173^{o} C$

Q. A gas at temperature 27∘C and pressure 30 atm. is allowed to expand to 1 atm pressure. If the volume becomes 10 times its initial volume, the final temperature becomes:

100∘C

373 K

373∘C

−173∘C

Ideal gas equation is PV=RT⇒PV∝T Hence, T1​P1​V1​​=T2​P2​V2​​ 30030V​=T2​1×10V​ T2​=30300×10​=100K=−173oC

Q. A gas at temperature $27^{\circ} C$ and pressure 30 atm. is allowed to expand to 1 atm pressure. If the volume becomes 10 times its initial volume, the final temperature becomes:

$100^{\circ} C$

$373^{\circ} C$

$- 173^{\circ} C$

Ideal gas equation is $P V = RT \Rightarrow P V \propto T$ Hence, $\frac{P _{1} V _{1}}{T _{1}} = \frac{P _{2} V _{2}}{T _{2}}$ $\frac{30 V}{300} = \frac{1 \times 10 V}{T _{2}}$ $T_{2} = \frac{300 \times 10}{30} = 100 K = - 173^{o} C$