A rigid tank of volume V is subdivided into two parts with volumes V1 = V/3 and V2 = 2V/3 using a rigid partition. Volume V1 contains an ideal gas at 800◦C and pressure P1 while volume V2 is completely evacuated. Now the partition between the two volumes is removed, upon which the ideal gas expands into the entire tank. Heat is then applied to the gas until its pressure becomes equal to its initial pressure P1.

Determine the final temperature of the gas.

Final temperature = 1893 °C

Explanation:

We are given;

T1 = 800◦C = 800 + 273K = 1073K

V1 = V/3

V2 = 2V/3

P1 = P2

For ideal gases;

PV = mRT or PV/RT = m

Thus applying it to the question;

Thus,

P1•V1 = mR•T1

Since V1 = V/3

Thus, T1 = P1•V/3mR - - - eq1

Similarly,

P2•V2 = mR•T2

V2 = 2V/3

T2 = P2•2V/3mR

Since P1 = P2, thus;

T2 = P1•2V/3mR - - - eq2

Combining equation 1 and 2,we have

T1 = (T2)/2

Thus, T2 = 2T1

T2 = 2(1083)

T2 = 2166K or 2166 - 273 = 1893°C

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