An ideal gas undergoes a constant temperature (isothermal) process in a closed system. The specific heat transfer and work are, respectivelyQuestion 9Select one:a.0, -Cv ΔTb.Cv ΔT, 0c.CP ΔT, R ΔTd.RT loge( v2 / v1 ), RT loge( v2 / v1 )e.none of the above
Question
An ideal gas undergoes a constant temperature (isothermal) process in a closed system. The specific heat transfer and work are, respectivelyQuestion 9Select one:a.0, -Cv ΔTb.Cv ΔT, 0c.CP ΔT, R ΔTd.RT loge( v2 / v1 ), RT loge( v2 / v1 )e.none of the above
Solution
The correct answer is d. RT loge( v2 / v1 ), RT loge( v2 / v1 )
Here's why:
In an isothermal process, the temperature of the system remains constant. This means that the change in temperature (ΔT) is zero.
The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. For an ideal gas in an isothermal process, the change in internal energy is zero (because ΔT is zero). Therefore, the heat added to the system (Q) is equal to the work done by the system (W).
For an ideal gas, the work done in an isothermal process can be calculated using the equation W = nRT loge( v2 / v1 ), where n is the number of moles of gas, R is the ideal gas constant, T is the temperature, and v1 and v2 are the initial and final volumes.
Since Q = W, the heat transfer is also equal to nRT loge( v2 / v1 ).
So, the correct answer is d. RT loge( v2 / v1 ), RT loge( v2 / v1 )
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