Question

One mole of oxygen gas is at a pressure of 5.90 atm and a temperature of 22.5°C.

(a) If the gas is heated at constant volume until the pressure triples, what is the final temperature?
°C

(b) If the gas is heated so that both the pressure and volume are doubled, what is the final temperature?
°C

Answer 1

A) Given pressure p1=5.90atm, temperature T1=22.5°c=22.5+273=295.5°K

Volume v1= constant, pressure p2=3p1, temperature T2=?, volume v2= v1(since v1 is constant)

Now by ideal gas law

P1×v1/T1=P2×v2/T2

Substituting all the values

P1×v1/T1=3p1×v1/T2

T2=3p1×v1×T1/p1v1

T2=3T1=3×295.5=886.5 °K

T2=886.5–273=613.5°c

B) Given pressure p1=5.90atm , pressure p2=2p1, volume v1

Volume v2=2v1, temperature T1= 22.5°c=22.5+273=295.5°K

Temperature T2=?

Now again by ideal gas law

P1×v1/T1=P2×v2/T2

Substituting all the value

P1×v1/T1=2p1×2v1/T2

T2=4×P1×v1×T1/P1×v1

T2=4T1

T2=4×295.5=1182°K

T2=1182–273=909°c