Question

Suppose that, when a spring was wound, 100 J of work was done on it but 15 J escaped to the surroundings as heat. The change in internal energy of the spring is​

Answer 1

Answer:

Suppose that, when a spring was wound, 100 J of work was done on it but 15 J escaped to the surroundings as heat. The change in internal energy of the spring is U= 100 J –15 J = + 85 J = 85 J

Answer 2

Therefore the change in the internal energy is 85 J.

Given:

The work done on the spring = 100 J

The heat transferred to the surroundings = 15 J

To Find:

The change in the internal energy of the spring (ΔU).

Solution:

The given question can be solved very easily as shown below.

Given that,

The work done on the spring = dW = 100 J

The heat transferred to the surroundings = dQ = 15 J

According to the first law of Thermodynamics,

Heat transferred = Work done + Change in internal energy

Sign convention:

For Work done:

Positive - if work is done by the system

Negative-  if work is done on the system

In the question, it is given that work is done on the spring so dW is 'negative'.

For Heat transfer:

Positive - if heat is transferred to the system

Negative - if heat is transferred to the surroundings

In the question, it is given that heat is transferred to the surroundings so dW is 'negative'

⇒ dQ = dW + ΔU

After applying the sign convention,

⇒ -dQ = -dW + ΔU

⇒ ΔU = dW - dQ

⇒ ΔU = 100 - 15 = 85

Therefore the change in the internal energy is 85 J.

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