Question

One mole of an ideal gas is heated from $0{}^\circ C$ to $100{}^\circ C$ at a constant pressure of 1 atmosphere. Calculate the work done in the process.
(A) -831.4 J
(B) 831.4 J
(C) 831.4 Cal
(D) 831.4 ergs

Answer 1

Ideal gas is a theoretical gas which is composed of many randomly moving point-sized moving particles which are not subjected to any interparticle interactions. The concept of an ideal gas is useful as it obeys ideal gas law.

Complete step by step solution:
-According to question,
Number of moles (n) = 1 mol
Pressure = 1 atmosphere
Initial temperature, ${{T}_{1}}=0{}^\circ C=273K$
Final temperature, ${{T}_{2}}=100{}^\circ C=373K$
-We know that,
Work done $=-P\Delta V...(1)$
Also, as the gas is an ideal gas, which means that it will follow the ideal gas law which says that,
$PV=nRT\Rightarrow P\Delta V=nR\Delta T...(2)$
-From equation (2), equation (1) can now also be written as-
$\begin{aligned} & =-nR\Delta T \\\ & =-1\times 8.314\times (373-273) \\\ & =-831.4J \\\ \end{aligned}$

So, the correct answer is option B.

Note: The classical thermodynamic properties of an ideal gas can be described by two equations of state and equations of the state is a thermodynamic equation relating the state of variables which described the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. The ideal gas law is an extension of experimentally discovered gas laws and can be derived from Boyle’s law, Charle’s law and Avagadro’s law. The empirical relationships between the pressure, the volume, the temperature, and the number of moles of a gas is given by the ideal gas law. It can be used to calculate any of these properties if the other three are known. The equation for ideal gas law is as follows-
Ideal gas equation $=PV=nRT$
where R is the gas constant, i.e $R=0.08206\dfrac{L.atm}{K.mol}=8.3145\dfrac{J}{K.mol}$
P is the pressure
V is the volume
T is the temperature
N is the amount of substance.