Question

Part 3/3 find the thermal energy transferred. Answer in units of KJ

Answer 1

0.0We are asked to determine the volume of a gas given the moles, the temperature, and the pressure. To do that, we use the following formula:

`PV=nRT`

Where:

`\begin{gathered} P=pressure \\ V=\text{ volume} \\ n=\text{ number of moles} \\ R=\text{ universal gas constant} \\ T=\text{ temperature} \end{gathered}`

Now, we substitute the values for the final state. Since the process is isothermally this means that the final temperature is the same as the initial temperature. we get:

`(1.8atm)V_f=(2mol)(8.31415(J)/(Kmol))(243K)`

We need to convert the pressure from atmospheres to Pascals. To do that we use the following conversion factor:

`1atm=101325Pa`

Multiplying by the conversion factor we get:

`1.8atm*(101325Pa)/(1atm)=182385Pa`

Now, we substitute the value in the formula:

`(182385Pa)V_f=(2mol)(8.3145*(J)/(Kmol))(243K)`

Solving the operations:

`(182385Pa)V_f=4040.847J`

Now, we divide both sides by 182385Pa:

`V_f=(4040.847J)/(182385Pa)`

Solving the operations:

`V_f=0.022m^3`

Therefore, the final volume is 0.022 cubic meters.

Part B. We are asked to determine the work done. To do that we will use the formula for isothermic work:

`W=nRT\ln((P_0)/(P_f))`

Where:

`P_0,P_f=\text{ initial and final pressure}`

Now, we plug in the values:

`W=(2mol)(8.31451(J)/(Kmol))(243K)\ln((0.21atm)/(1.8atm))`

Now, we solve the operations:

`W=-8681.51J`

Therefore, the work done is -8681.51 Joule. To convert to kilojoules we divide by 1000:

`W=-8681.51J*(1kJ)/(1000J)=-8.68kJ`

Part 3. In an isothermic process the change in internal energy is zero, therefore, according to the first law of thermodynamics we have:

`Q-W=0`

Therefore:

`Q=W`

Therefore, the amount of heat is equal to the amount of work. Therefore, the thermal energy transferred is:

`Q=-8.68kJ`