Question

A block of copper whose expansivity, β, is 48.0 x 10^-6 k^-1 and isothermal elasticity, ET ,
is 1.30 x 10^11 Nm^-2 is at atmospheric pressure and a temperature of 0°C. Its temperature is
raised to 10°C. Calculate the final pressure when volume is kept constant. Express your
answer in units of atmospheric pressure (atm).

Answer 1

Answer on Question #50647-Physics-Molecular Physics-Thermodynamics

A block of copper whose expansivity, $\beta$, is $48.0 \cdot 10^{-6} k^{-1}$ and isothermal elasticity, $E_{T}$, is $1.30 \cdot 10^{11} Nm^{-2}$ is at atmospheric pressure and a temperature of $0{}^{\circ}\mathrm{C}$. Its temperature is raised to $10{}^{\circ}\mathrm{C}$. Calculate the final pressure when volume is kept constant. Express your answer in units of atmospheric pressure (atm).

Solution

For an isochoric process, we have

$$p_{2} - p_{1} = \beta E_{T} (T_{2} - T_{1}).$$

On substituting the values of $\beta, E_{T}, (T_{2} - T_{1})$, we get

$$p_{2} - p_{1} = 48.0 \cdot 10^{-6} k^{-1} \cdot 1.30 \cdot 10^{11} Nm^{-2} (10K) = 624 \cdot 10^{5} Nm^{-2} = 624 \text{ atm}.$$

so that final pressure $p_{2}$ is

$$p_{2} = (624 + 1) \text{ atm} = 625 \text{ atm}.$$

That is, to keep the volume of the copper block constant when its temperature is raised from $0{}^{\circ}\mathrm{C}$ to $10{}^{\circ}\mathrm{C}$, one must increase the pressure to 625 atm.

**Answer: 625 atm.**

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