Chapter 12 - Gases and the Kinetic-Molecular Theory - Exercises - Charles's Law: The Volume-Temperature Relationship - Page 440: 23

a) 229 K or -44$^{\circ}$ C b) 76 K or -197$^{\circ}$ C

Work Step by Step

a) $T_{1}$ = (32+273) K = 305 K Let's assume $V_{1}$ = 4 V Then $V_{2}$ = 3 V (decreased by 25%) According to Charles's Law, $\frac{V_{1}}{T_{1}}$ = $\frac{V_{2}}{T_{2}}$ Or $T_{2}$ = $\frac{V_{2}\times T_{1}}{V_{1}}$ = $\frac{3V\times305K}{4V}$ $\approx$ 229 K b) Here only $V_{2}$ is changed. $V_{2}$ = V if $V_{1}$ = 4V $T_{2}$ = $\frac{V\times 305 K}{4V}$ $\approx$ 76 K .

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