Question

1. On a hot day in Las Vegas an empty diesel truck (capacity = 40,000 L) is filled with diesel fuel [ = 9.1 x 10-4 (Co)-1] at a rate of 200 litres per minute. The truck then travels to the customer in Payson, Utah during which time the temperature drops by 23 K.

How long does it take to fill the truck?

A. 3 hours and 20 minutes

B. 2 hours

C. 1 hour

D. 10 hours

2. In the scenario described in question 1, what volume of diesel fuel is delivered to the customer?

A. 40,874 litres

B. 39,126 litres

C. 40,000 litres

D. 20,000 litres

3. A gold ring has internal diameter 19 mm. at a room temperature of 20 C^o. It is placed in hot water in order to raise its temperature to 80 C^o. What is its new internal diameter? [For gold, α = 14.2 x 10^-6 (C^o)^-1 ]

A. 19.016 mm

B. 18.984 mm

C. 19.016 mm

D. There is no change in diameter

Answer 1

1.

Time taken to fill the truck will be given by:

time = Volume of truck/flow rate

Volume of truck = 40000 L

flow rate = 200 L/min

So,

time = 40000 L/(200 L/min) = 200 min

1 hr = 60 min, So

time = 3 hr 20 min

Correct option is A.

2.

Now Volume of truck will decrease due to temperature drop, which will be given by:

dV = V0*beta*dT

beta = Volume expansion coefficient = 9.1*10^-4 /C

dT = 23 K

V0 = 40000 L = 40 m^3,

So

dV = 40000*9.1*10^-4*23 = 837.2 L

Amount of fuel delivered = Vf = Vi - dV = 40000 - 837.2 = 39162.8 L

from your given option, since temperature is dropped, So volume will also drop and from given options, Option B is nearest to the above value.

Correct option is B.

3.

Increase in diameter due to temperature increase will be

dD = D0*alpha*dT

D0 = initial diameter = 19.mm

alpha = linear expansion coefficient

dT = Tf - Ti = 80 - 20 = 60 C

dD = 19*14.2*10^-6*(80 - 20) = 0.016 mm

So new diameter will be

D_new = D0 + dD = 19 + 0.016 = 19.016 mm

Correct option is A.

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