Question

When heat energy of 1500 J is supplied to a gas at constant pressure of $2.1\times {{10}^{5}}N{{m}^{-2}}$ then there is an increase in its volume up to $2.5\times {{10}^{-3}}{{m}^{3}}$ . The increase in internal energy of the gas (in joule) is :
A 450 J
B 525 J
C 975 J
D 2025 J

Answer 1

The energy contained within a thermodynamic system is known as its internal energy. It's the amount of energy required to build or prepare a system in any given internal condition. It excludes the kinetic energy of the system's motion as a whole, as well as the potential energy of the system as a whole owing to external force fields, which includes the energy of displacement of the system's surroundings. It maintains track of the system's energy gains and losses as a result of changes in its internal condition. The difference between a reference zero established by a standard condition and the internal energy is measured.

Complete step by step solution:
Internal energy is a broad characteristic that cannot be directly quantified. Transfers of matter or energy as heat, as well as thermodynamic work, are the thermodynamic processes that characterise internal energy. Changes in the system's many variables, such as entropy, volume, and chemical composition, are used to measure these processes. Considering all of the system's inherent energies, such as the static rest mass energy of its component materials, isn't always essential.
The first law of thermodynamics describes the change in internal energy as the difference between the energy contributed to the system as heat and the thermodynamic work done by the system on its surroundings when matter transfer is blocked by impermeable enclosing walls. The system is considered to be isolated if no matter nor energy passes through the enclosing walls, and its internal energy cannot alter. Internal energy is an analogous representation of entropy, both cardinal state functions of just extensive state variables, and provides the whole thermodynamic information of a system.

The Change in internal energy is given by $=$ Heat energy added $+$ work done
$\Delta \mathrm{U}=1500-\left(2.1 \times 10^{5}\right) \times\left(2.5 \times 10^{-3}\right)$
$\Rightarrow \Delta \text{U}=1500-525=975~\text{J}$
Hence option C is correct.

Note:
Internal energy does not include the energy generated by a system's overall motion or position. That is, any kinetic or potential energy held by the body as a result of its mobility or position in external gravitational, electrostatic, or electromagnetic fields is excluded. It does, however, take into account the energy contribution of such a field due to the coupling of the object's internal degrees of freedom with the field. In this scenario, the field is added as an extra external parameter in the object's thermodynamic description.