Chemistry, 25.09.2019 01:10 litzy90

Consider 1 kg of nh3 that was compressed from 2.5 bar and 30°c to 5.0 bar in a well-insulated compressor. determine the (a) final temperature in c and (b) the work required in kj.

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Answer from: AlexRavenwood127

Explanation:

(a) The given data is as follows.

mass = 1 kg = 1000 g (as 1 kg = 1000 g)

Molar mass of $NH_{3}$ = 17 g/mol

$P_{1}$ = 2.5 bar = $2.5 \times 10^{5} Pa$ (as 1 bar = $10^{5} Pa$ )

$P_{2}$ = 5 bar = $5 \times 10^{5} Pa$

$T_{1} = 30^{o}C$ = 30 + 273 = 303 K

For adiabatic process, $PV^{\gamma}$ = constant = k

$\gamma$ = 1.33 = $\frac{C_{p}}{C_{v}}$

$P_{1}V_{1}^{\gamma} = P_{2}V_{2}^{\gamma}$

$(\frac{V_{2}}{V_{1}})^{\gamma} = \frac{P_{1}}{P_{2}}$

$\frac{V_{2}}{V_{1}} = (\frac{P_{1}}{P_{2}})^{\frac{1}{\gamma}}$

$V_{2} = (\frac{2.5 \times 10^{5}}{5 \times 10^{5}})^{\frac{1}{1.33}} \times \frac{nRT_{1}}{P_{1}}$ (as PV = nRT)

= $(\frac{2.5}{5})^{\frac{1}{1.33}} \times \frac{58.82 \times 8.314 J/mol K \times 303 K}{2.5 \times 10^{5}}$

= 0.352 $m^{3}$

Also, w = $\frac{P_{1}V_{1} - P_{2}V_{2}}{\gamma - 1}$

= $\frac{2.5 \times 10^{5} \times 0.5927 - 5 \times 10^{5} \times 0.352}{1.33 - 1}$

= -84318.2 J

As 1 kJ = 1000 J. So, -84318.2 J = -84.318 kJ

Hence, the work required in kJ is -84318.2 J.

(b) It is known that for adiabatic system Q = 0,

$\Delta U = Q - w$

$nC_{v}dT$ = -w

dT = $\frac{-w}{nC_{v}}$

= $\frac{84318.2}{58.82 \times 1.6}$

= 895.93 K

We known that dT = $T_{1} - T_{2}$

so, 895.93 = 303 K - $T_{2}$

$T_{2}$ = (895.93 - 303)K

= 592.93 K

= (592.93 - 273.15)^{o}C

= $319.78^{o}C$

Hence, the final temperature is $319.78^{o}C$ .

Answer from: Quest

first one is the correct answer

Answer from: Quest

in 1783 cavendish was working with his hydrogen gas and found that when he burned it and condensed the vapor it was water. this was very significant since it disproved the greek theory of elements completely since water was not a simple substance but the product of two gases. it was lavoisier who hearing of the experiment gave cavendish's gas the name hydrogen ("water-producer") and added that hydrogen burned by combining with oxygen and that water was a hydrogen-oxygen combination.

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Consider 1 kg of nh3 that was compressed from 2.5 bar and 30°c to 5.0 bar in a well-insulated compre...

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