Hello …..

At 27 degree celcius , a gas is suddenly compressed such that its internal energy increase by 40 joule. What is the amont of work done............. Please explain with steps .

To determine the amount of work done on the gas during its compression, we can use the first law of thermodynamics, which 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. In mathematical terms, this can be expressed as:

First Law of Thermodynamics

The equation can be written as:

ΔU = Q - W

Where:

• ΔU = Change in internal energy
• Q = Heat added to the system
• W = Work done by the system

Given Information

In your scenario, we know:

• ΔU = +40 joules (the internal energy increases)
• Since the gas is compressed, we can assume that no heat is added to the system (Q = 0) during this rapid process.

Applying the First Law

Substituting the known values into the first law equation:

40 J = 0 - W

Rearranging this gives us:

W = -40 J

Interpreting the Result

The negative sign indicates that work is done on the gas. In other words, when the gas is compressed, energy is transferred to it, which increases its internal energy. Therefore, the amount of work done on the gas is 40 joules.

Summary

In summary, when the gas is compressed and its internal energy increases by 40 joules, the work done on the gas is 40 joules. This scenario illustrates how energy conservation principles apply in thermodynamic processes, highlighting the relationship between work, heat, and internal energy changes.