While camping, you decided to take a warm bath. You find a fresh pool of rainwat
ID: 1074197 • Letter: W
Question
While camping, you decided to take a warm bath. You find a fresh pool of rainwater 0.5m deep x 0.3m wide x 1.6m long that has collected in a rocky cavity. The water temperature is 12°C and you would like to heat it up to 45°C. Your plan is to use your campfire to heat rocks to a temperature of 180°C and then roll the hot rocks into the water until the temperature is right. How many rocks will you need if the average mass of the rocks is 1.5 kg and the average specific heat of the rocks is 800 J/ kg? Assume that the cavity that contains the water is insulated (no heat loss) and can hold as many rocks as needed without spilling over.
Explanation / Answer
volume of pool = l*b*h
= 0.5*0.3*1.6
= 0.24 m^3 (1 m^3 = 10^3 L)
= 0.24*10^3 L ( 1 L = 10^3 ml)
= 0.24*10^6 ml
density(d) = 1 g/cc
mass of water(m) = 0.24*10^6 g
amount of heat required to heat water = m*s*DT
= 0.24*10^6*4.184*(45-12)
= 33137.28 kj
heat given by each rock to water to bring temperature up to 45 c = m*s*dT
= 1.5*800*(180-45)
= 162.0 kj
no of rocks required = 33137.28/162 = 204.55
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