1a) A gaseous system absorbs 97 J of heat and increases its internal energy by 8

Question

1a) A gaseous system absorbs 97 J of heat and increases its internal energy by 85 J. Which of the following statements is correct? The volume of the system decreases and a positive amount of work is done. The volume of the system increases and a positive amount of work is done. The volume of the system increases and a negative amount of work is done. The volume of the system remains constant and no work is done The volume of the system decreases and a negative amount of work is done. 1b)A 27.1-g piece of iron initially at 92.9 °C is submerged into 194.4 g of water at 18.1 °C. What is the final temperature of the metal once the metal and water reaches thermal equilibrium? The specific heats of iron and water are 0.449 J/g·°C and 4.18 J/g·°C, respectively.

Explanation / Answer

1a) q =+97 J
     U = +85J
   U = q + W , W =P V = 85-97 = -12 J of work is done

The volume of the system increases and negative amount of work is done

1b) q lost = qgain , (mcpt)iron = (mcpt)water
   27.1 * (92.9 - x) * 0.449 = 194.4 * (x- 18.1) * 4.18
   12.1679 ( 92.9 - x) = 812.592 (x- 18.1)
   1130.3971 - 12.1679x = 812.592x - 14707.9152
15838.3123 = 824.7599 x
   x = 19.2035
The final temperature of the metal once the metal reaches thermal equilibrium is 19.2 oC

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