TS EAMCET · Physics · Thermal Properties of Matter

A metal ball initially at pressure of $10^{5} P_{a}$ is heated from $20 ° C$ to $127 ° C$ keeping its volume constant. The coefficient of linear expansion of metal is $10^{- 5} (° C^{- 1})$ and bulk modulus of metal is $2 \times 10^{11} N m^{- 2}$ . The pressure inside the ball becomes

A $2 \times 10^{8} Pa$
B $6 \times 10^{8} Pa$
C $1 \times 10^{9} Pa$
D $4 \times 10^{8} Pa$

Verified Solution

Answer & Solution

Correct Answer

(B) $6 \times 10^{8} Pa$

Step-by-step Solution

Detailed explanation

The ball tries to expand its volume. But it is kept in the same volume. So it is kept at a constant volume. So the stress that arises is defined as: B=P∆VV, now we know that change in volume due to thermal expansion,…

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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A metal ball initially at pressure of 105 Pa is heated from 20°C to 127°C keeping its volume constant. The coefficient of linear expansion of metal is 10-5°C-1 and bulk modulus of metal is 2×1011 N m-2. The pressure inside the ball becomes

Step-by-step Solution

A metal ball initially at pressure of $10^{5} P_{a}$ is heated from $20 ° C$ to $127 ° C$ keeping its volume constant. The coefficient of linear expansion of metal is $10^{- 5} (° C^{- 1})$ and bulk modulus of metal is $2 \times 10^{11} N m^{- 2}$ . The pressure inside the ball becomes