Question

When the pressure of a fixed mass of gas is increased to 5 atmospheric pressure the temperature increases from —70°c to 130°c.what is the ratio of the initial pressure

Answer 1

Answer on Question #73759, Physics / Molecular Physics | Thermodynamics

Question. When the pressure of a fixed mass of gas is increased to 5 atmospheric pressure the temperature increases from $-70{}^{\circ}C$ to $130{}^{\circ}C$. What is the ratio of the initial pressure.

Given.

$$p_{fin} = 5 \text{ atm} = 506625 \text{ Pa}; T_{in} = -70{}^{\circ} = 203 \text{ K}; T_{fin} = 130{}^{\circ} \text{C} = 403 \text{ K}.$$

Find.

$$p_{in} - ?.$$

Solution.

If $V = \text{const} \ (V_{in} = V_{fin})$ then

$$\frac{p_{in} V_{in}}{T_{in}} = \frac{p_{fin} V_{fin}}{T_{fin}} \rightarrow p_{in} = \frac{p_{fin} V_{fin} T_{in}}{V_{in} T_{fin}} = \frac{p_{fin} T_{in}}{T_{fin}} = \frac{506625 \cdot 203}{403} = 255198 \text{ Pa}$$

Answer. $p_{in} = 255198 \text{ Pa}$.

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