TS EAMCET · Physics · Thermodynamics

$500 g$ of water is heated from $30 ° C$ to $90 ° C .$ What is the change in its internal energy? (Specific heat of water is $4184 J {kg}^{- 1} K^{- 1}$ )

A $1.25 \times 10^{5} J$
B $2.0 \times 10^{5} J$
C $1.3 \times 10^{4} J$
D $2.0 \times 10^{4} J$

Verified Solution

Answer & Solution

Correct Answer

(A) $1.25 \times 10^{5} J$

Step-by-step Solution

Detailed explanation

The formula of change in internal energy in terms of molar specific heat at constant volume and, change in temperature, dU=mCVT2-T1, given, dU=5001000×418490°-30°=125520 J. So the change in internal energy, dU=1.25×105 J

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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500 g of water is heated from 30°C to 90°C. What is the change in its internal energy? (Specific heat of water is 4184 J kg-1 K-1)

Step-by-step Solution

$500 g$ of water is heated from $30 ° C$ to $90 ° C .$ What is the change in its internal energy? (Specific heat of water is $4184 J {kg}^{- 1} K^{- 1}$ )