Question 361: Thermodynamics & KTG

Question

The temperature of equal masses of three different liquids x, y and z are 10$$^\circ$$C, 20$$^\circ$$C and 30$$^\circ$$C respectively. The temperature of mixture when x is mixed with y is 16$$^\circ$$C and that when y is mixed with z is 26$$^\circ$$C. The temperature of mixture when x and z are mixed will be :

Accepted Answer

when x and y are mixed, T
f
1
= 16$$^\circ$$C
m
1
s
1
T + m
2
s
2
T
2
= (m
1
s
1
+ m
2
s
2
)Tf
1
s
1
$$	imes$$ 10 + s
2
$$	imes$$ 20 = (s
1
+ s
2
) $$	imes$$ 16
s
1
= $${2 \over 3}$$s
2
.... (i)
when y and z are mixed, T
f
2
= 26$$^\circ$$C
m
2
s
2
T + m
3
s
3
T
3
= (m
3
s
3
+ m
3
s
3
)Tf
2
s
2
$$	imes$$ 20 + s
3
$$	imes$$ 30 = (s
2
+ s
3
) $$	imes$$ 26
s
3
= $${3 \over 2}$$s
2
..... (ii)
when x and z are mixed
m
1
s
1
T
1
+ m
3
s
3
T
3
= (m
1
s
1
+ m
3
s
3
)Tf
$${2 \over 3}$$s
2
$$	imes$$ 10 + $${2 \over 3}$$s
2
$$	imes$$ 20 = $$\left( {{2 \over 3}{s_2} + {3 \over 2}{s_2}} ight){T_f}$$
T
f
= 23.84$$^\circ$$C

Answer

28.32$$^\circ$$C

Answer

25.62$$^\circ$$C

Answer

23.84$$^\circ$$C

Answer

20.28$$^\circ$$C

Thermodynamics & KTG

The temperature of equal masses of three different liquids x, y and z are 10$^\circC, 20^\circC and 30^\circC respectively. The temperature of mixture when x is mixed with y is 16^\circC and that when y is mixed with z is 26^\circ$C. The temperature of mixture when x and z are mixed will be :

Choose the correct answer: