Figure 3.102 shows two containers, each of volume 2 × 1 0 − 4 m 3 , holding equal amounts of an ideal gas, joined by a U-tube containing mercury. The initial pressure and temperature of both are 75 cm

Question

Figure 3.102 shows two containers, each of volume $2 \times 1 0^{- 4}$ $m^{3}$ , holding equal amounts of an ideal gas, joined by a U-tube containing mercury. The initial pressure and temperature of both are 75 cm of Hg and 300 K. The mercury levels are equal. The containers are supplied 5 J and 10 J of heat respectively. Find the final difference in the mercury heights. Neglect the volume of the tubes. $C_{v} = 12.5$ J $m o l^{- 1}$ $K^{- 1}$ .

TestHub · Accepted Answer

n = RT P V ​ = 8.314 × 300 1 0 5 × 2 × 1 0 − 4 ​ = 8.0 × 1 0 − 3 mol. Volume is fixed, so Δ T = n C v ​ Q ​ : Δ T 1 ​ = 50 K, Δ T 2 ​ = 100 K. Δ P = P T Δ T ​ : 12.5 cm Hg and 25 cm Hg. Height difference = 25 − 12.5 = 12.5 cm.

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