Gas Heated at Constant Pressure

When a gas is heated at constant pressure, it undergoes a process known as isobaric heating. In this process, the pressure of the gas remains constant while its volume and temperature change. The heat supplied to the gas is used to increase its temperature, perform external work, and increase its internal energy.

Percentage of Heat Supplied Used for External Work

To determine the percentage of heat supplied used for external work, we need to understand the concept of heat transfer and work done in thermodynamics.

Heat Transfer
Heat transfer is the process of energy transfer from a higher temperature region to a lower temperature region. In the case of isobaric heating, heat is transferred to the gas from an external source, increasing its internal energy.

Work Done
Work done in thermodynamics is the energy transfer resulting from a force acting on an object over a distance. In the case of isobaric heating, the gas expands against a constant pressure, resulting in the performance of external work.

First Law of Thermodynamics
The first law of thermodynamics states that the change in internal energy of a system is equal to the heat supplied to the system minus the work done by the system.

Calculation of External Work
The work done by the gas during isobaric heating can be calculated using the equation:

Work = Pressure x Change in Volume

Since the pressure remains constant in this case, the equation simplifies to:

Work = Constant Pressure x Change in Volume

Calculation of Heat Supplied
The heat supplied to the gas during isobaric heating can be calculated using the equation:

Heat = Change in Internal Energy + Work

Since we are interested in the percentage of heat supplied used for external work, we can rearrange the equation as follows:

Percentage of Heat Used for External Work = (Work / Heat) x 100

Substituting Values
In the given problem, it is stated that y = 4/3 for the gas. This means that the ratio of the specific heat capacities, γ (gamma), is equal to 4/3.

For an ideal gas, the relationship between γ and the percentage of heat used for external work is given by the equation:

Percentage of Heat Used for External Work = (γ - 1) / γ * 100

Substituting the value of γ = 4/3 into the equation, we can calculate the percentage of heat supplied used for external work.

Simplifying the Equation
To simplify the equation, we can multiply the numerator and denominator by 3 to get:

Percentage of Heat Used for External Work = (4 - 3) / 4 * 100

Simplifying further, we have:

Percentage of Heat Used for External Work = 1 / 4 * 100

Percentage of Heat Used for External Work = 25%

Explanation
Therefore, in this case, 25% of the heat supplied to the gas is used to perform external work. The remaining 75% of the heat is used to increase the internal energy of the gas. This percentage is determined by the specific heat capacity ratio, which represents the ability of the gas to convert heat into work.