A gas is compressed from 600 cm^3 to 200 cm^3 at a constant pressure of 400 kPa. At the same tim

step 1 Hello friends here is given. A gas is to be compressed from initial volume of 600 cm cube flow p

A gas is compressed from 600 cm^3 to 200 cm^3 at a constant...

A gas is compressed from $600 \mathrm{cm}^{3}$ to $200 \mathrm{cm}^{3}$ at a constant pressure of $400 \mathrm{kPa}$. At the same time, $100 \mathrm{J}$ of heat energy is transferred out of the gas. What is the change in thermal energy of the gas during this process?

Key Concepts

Change in Internal (Thermal) Energy

The change in internal energy (?U) represents the net change in a system's thermal energy due to heat transfer and work interactions. By rearranging the first law to ?U = Q - W (using the convention for work done by the system), one can determine how the internal energy changes during a thermodynamic process.

Sign Conventions in Thermodynamics

Sign conventions are crucial for correctly applying the first law. Heat added to the system is taken as positive (Q > 0), and heat removed is negative (Q < 0). Similarly, work done by the system is positive (W > 0), while work done on the system is negative (W < 0). This convention helps in correctly accounting for energy transfers.

Work Done by a Gas at Constant Pressure

When a gas is compressed or expanded at constant pressure, the work done by (or on) the gas is calculated as W = P?V, where ?V is the change in volume. In processes where the volume decreases (compression), the work done by the gas is negative, indicating that work is done on the system.

First Law of Thermodynamics

This principle states that energy is conserved in a closed system and can be expressed as Q = ?U + W, where Q is the heat added to the system, ?U is the change in internal (thermal) energy, and W is the work done by the system. It provides a framework to analyze energy exchanges in thermodynamic processes.

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