An ideal gas initially at 50ºC and pressure P 1 = 100 kPa occupies a volume V 1

Question

An ideal gas initially at 50ºC and pressureP1 = 100 kPa occupies a volumeV1 = 3 L. It undergoes a quasi-static,isothermal expansion until its pressure is reduced to 50 kPa. Howmuch heat enters the gas during this process? R = 8.314J/mol·K = 8.206 L·atm/mol·K.
An ideal gas initially at 50ºC and pressureP1 = 100 kPa occupies a volumeV1 = 3 L. It undergoes a quasi-static,isothermal expansion until its pressure is reduced to 50 kPa. Howmuch heat enters the gas during this process? R = 8.314J/mol·K = 8.206 L·atm/mol·K.

Explanation / Answer

You need three things: . 1.   since temperature is constant, thevolume doubles when the pressure is halved. Final volume is 6L. . 2.   First law of thermosays:           E = Q - W      but since E is zero for an isothermal process, Q =W                  where   W is the work done by the gas. . 3. Work done by an ideal gas in an isothermalprocess is    W = n R T ln(Vf / Vi) . And using the idea that   p V = n R T  you can calc work: .       W = p V ln(6/3) = 100 * 3 * ln2 =    208Joules    so this is also Q, the heat that enteredthe gas.

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