In a scenario where 12 joules of heat is added to an ideal gas that does 8 joules of work, by how much does the internal energy of the gas change?

In a scenario where 12 joules of heat is added to an ideal gas that does 8 joules of work, by how much does the internal energy of the gas change?

• A. Increased by 20 joules
• B. Increased by 4 joules
• C. Not changed
• D. Decreased by 4 joules

Answer: (B)

To determine how much the internal energy of the gas changes when heat is added and work is done, we can use the first law of thermodynamics. This law states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W). In this scenario, we know that: - Heat added to the gas (Q) = 12 joules - Work done by the gas (W) = 8 joules Using the first law of thermodynamics, the equation becomes: ΔU = Q - W Substituting in the values, we get: ΔU = 12 joules - 8 joules ΔU = 4 joules This result shows that the internal energy of the gas increases by 4 joules. Hence, the correct answer is that the internal energy of the gas has increased by 4 joules. This process highlights how energy is conserved in thermodynamic systems, allowing us to account for the heat added and the work done in determining the change in internal energy.

To determine how much the internal energy of the gas changes when heat is added and work is done, we can use the first law of thermodynamics. This law states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W).

In this scenario, we know that:

• Heat added to the gas (Q) = 12 joules

• Work done by the gas (W) = 8 joules

Using the first law of thermodynamics, the equation becomes:

ΔU = Q - W

Substituting in the values, we get:

ΔU = 12 joules - 8 joules

ΔU = 4 joules

This result shows that the internal energy of the gas increases by 4 joules. Hence, the correct answer is that the internal energy of the gas has increased by 4 joules. This process highlights how energy is conserved in thermodynamic systems, allowing us to account for the heat added and the work done in determining the change in internal energy.