# If 40 kJ heat is transferred from gas and work done to compress gas is 20 kJ then what is the change in internal energy

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If 40 kJ heat is transferred from gas and work done to compress gas is 20 kJ then what is the change in internal energy
1. 60 kJ increase
2. 20 kJ decrease
3. 60 kJ decrease
4. 20 kJ increase

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Correct Answer - Option 2 : 20 kJ decrease

Concept:

The first law of thermodynamics is a restatement of the law of conservation of energy. It states that energy cannot be created or destroyed in an isolated system; energy can only be transferred or changed from one form to another.

When heat energy is supplied to a gas, two things may occur:

• The internal energy of the gas may change
• The gas may do some external work by expanding

According to the first law of Thermodynamics:

ΔQ = ΔW + ΔU ...(i)

i.e., When a process is executed by a system, the change in stored energy of the system is numerically equal to the net heat interaction minus the network interaction during the process:

Here, ΔQ = heat exchange, ΔW = work done due to expansion, ΔU = internal energy of the system.

Sign convention:

ΔQ = Positive (Heat supplies to the system)

ΔQ = Negative (Heat rejected from the system)

ΔW = Positive (Work done by the system)

ΔW = Negative (Work done on the system).

Calculation:

Given:

ΔQ = -40 kJ, ΔW = -20 kJ

Using Equation (i)

ΔQ = ΔW + ΔU

-40 = -20 + ΔU

ΔU = -20 kJ

20 kJ Decrease in internal energy.