Question

Imagine that you have two cups, one containing 1540 g of water and the other one containing some amount of an unknown liquid. The specific heat of water is 4.19 J/g·°C, and the specific heat of the unknown liquid is 7.03 J/g·°C. You use two identical immersion heaters to heat the water and the unknown liquid simultaneously. Assume that all the heat from the heater is used to heat the content of the cups.

(a) You started heating the water and the unknown liquid at the same time. If the temperature of the water was increased from 23.7 °C to 40.8 °C while the temperature of the unknown liquid is increased from 23.7 to 31.5 °C, what was the mass of the unknown liquid in the cup?
________-grams

(b) If you used 102 W heaters to heat the liquids in part (a), how long did you heat the liquids?
________-minutes

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You and your friend went to kitchen to boil water. The specific heat of water is 4.19 J/g °C, and the latent heat of vaporization of water is 2260 J/g.

(a) You poured 179 gram of water to a container and put the container on a 212 W electric heater. After turning on the heater, you went away for 22 minutes to do something else. The container was not covered so that the vaporized water was removed from the container. When you came back to the kitchen 22 minutes later to check the water, the container had 83.0 gram of water left in it boiling. What was the temperature of your water when when you turned on the heater?
________-°C

(b) Your friend wanted her own boiling water. She poured 426 gram of water into another container and put her own electric heater at the same time as you did. The initial temperature of her water was the same as yours. When you came back to the kitchen to check the water in 22 minutes, there was 301.2 gram of water left in her container. What was the power of your friend's electric heater?
__________-W

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Consider a mass lifting heat engine like the one you experimented with in the lab. The pressure, volume, and temperature data for the heat engine are shown in the table below:
.

State	Pressure	Volume	Temperature [°C]
a	pa	va	2.0
b	pb	vb	2.0
c	pc	vc	40.0
d	pd	vd	40.0
a´=a	pa	va	2.0

In the above table, p_a = p_d and p_b = p_c. Also v_d - v_a = v_c - v_b.
The diameter of the piston is is measured to be 14.15 mm.
a) If the work done by the engine in one cycle is 6.0 mJ, and the pressure difference between the state b and d is 5.0 kPa, what would be the volume change as the engine moves from the state d to a?

a) 1.2 m³ b) 1.2 ml c) 1.2x10^-3 ml

b) Then, how high was the object lifted?

a) 0.0076 m b) 0.76 m c) 3.1 m

Answer 1

I will do only 4 parts,

a) Heat supplied is same

( 1540)(4.19) ( 40.8- 23.7) = m ( 7.03) ( 31.5- 23.7)

mass of unknown liquids= 2012.245 gm apprx

b) power = heat/time

time= ( 110339.46 J/ 102) =18.029 mon

c) let the initial tem of water = T

heat suplied = P x T= 212 ( 22x 60 ) = 279840 J

279840 = 179 x 4.19 ( 100 -T) + 2260 ( 179- 83)

179 ( 4.19 ) ( 100-T) = 62880

100-T = 62880/ 750.01

100-T = 83.83

T = 16.16 degree C

d) heat = 426 (  4.19 ) ( 100- 16.16 ) + 124.8 ( 2260) = 431697. 3696 J

power = ( 431697. 3696 J)/ (22x 60 )= 327 W