Question 408: Thermodynamics & KTG

Question

A metal ball of mass 0.1 kg is heated upto 500
o
C and dropped into a vessel of heat capacity 800 JK
–1
and containing 0.5 kg water. The initial temperature of water and vessel is 30
o
C. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg
–1
and 400 Jkg
–1
K
–1

Accepted Answer

0.1 $$ 	imes $$  400 $$ 	imes $$ (500 $$-$$ T) = 0.5 $$ 	imes $$ 4200 $$ 	imes $$ (T $$-$$ 30) + 800 (T $$-$$ 30)
$$ \Rightarrow $$  40(500 $$-$$ T) = (T $$-$$ 30) (2100 + 800)
$$ \Rightarrow $$  20000 $$-$$ 40T = 2900 T $$-$$ 30 $$ 	imes $$ 2900
$$ \Rightarrow $$  20000 + 30 $$ 	imes $$ 2900 = T(2940)
T = 30.4
o
C
$${{\Delta T} \over T} 	imes 100$$ = $${{6.4} \over {30}} 	imes 100$$
$$ \simeq $$ 20%

Answer

20%

Answer

25%

Answer

15%

Answer

30%

Thermodynamics & KTG

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