JEE MAIN - Physics (2017 (Offline) - No. 15)
An external pressure P is applied on a cube at 0oC so that it is equally compressed from all sides. K is the
bulk modulus of the material of the cube and $$\alpha$$ is its coefficient of linear expansion. Suppose we want to
bring the cube to its original size by heating. The temperature should be raised by:
$${P \over {3\alpha K}}$$
$${P \over {\alpha K}}$$
$${3 \alpha \over {P K}}$$
3PK$$\alpha$$
Explanation
As we know, Bulk modulus
K = $${{\Delta P} \over {\left( {{{ - \Delta V} \over V}} \right)}}$$
$$ \Rightarrow $$ $${{{\Delta V} \over V} = {P \over K}}$$
V = V0(1 + $$\gamma $$$$\Delta $$t)
$${{{\Delta V} \over {{V_0}}} = \gamma \Delta t}$$
$$ \therefore $$ $${{P \over K} = \gamma \Delta t}$$
$$ \Rightarrow $$ $${\Delta t = {P \over {\gamma K}}}$$ = $${{P \over {3\alpha K}}}$$
K = $${{\Delta P} \over {\left( {{{ - \Delta V} \over V}} \right)}}$$
$$ \Rightarrow $$ $${{{\Delta V} \over V} = {P \over K}}$$
V = V0(1 + $$\gamma $$$$\Delta $$t)
$${{{\Delta V} \over {{V_0}}} = \gamma \Delta t}$$
$$ \therefore $$ $${{P \over K} = \gamma \Delta t}$$
$$ \Rightarrow $$ $${\Delta t = {P \over {\gamma K}}}$$ = $${{P \over {3\alpha K}}}$$
Comments (0)
