Question

(b) Use the first law of thermodynamic to calculate AU for the following situations: (i) A coiled spring unwinds producing 153 J of work and losing 37 J as heat to friction (1 mark) (ii) An insulated bucket of water is stirred by a paddle, which provides 289 J of work. (1 mark) (iii) Adding 1 kJ of heat to a sample of gas in an isovolumetric process. (1 mark) (iv) The isothermal compression of a gas from 26 L to 5 L. (1 mark) (v) The isobaric expansion of a gas from 5 L to 18 L at a constant pressure of 950 kPa caused by the addition of 15.6 kJ of heat.

Answer 1

Answer:

(i) ΔU = 116 J

(ii) ΔU = 289 J

(iii) ΔU = 1 KJ

(iv) ΔU = 0 J

(v) ΔU = 3.25 KJ

Explanation:

first law:

• ΔU = Q + W

(i) W = 153 J;  Q = - 37 J ( Q ( - ), losing friction )

⇒ ΔU = 153 - 37 = 116 J

(ii) W = 289 J; Q = 0 ( insulated)

⇒ ΔU = W = 289 J

(iii) Q = 1 KJ , W = 0 ( isovolumetric process)

⇒ ΔU = Q = 1 KJ

(iv) isothermal ( constant temperature )

• ΔU = Cv * ΔT

∴ ΔT = 0° ( isothermal )

⇒ ΔU = 0 J

(v) isobaric ( constant pressure )

⇒ ΔU = Q + W

∴ Q = 15.6 KJ

∴ W = - ∫ P dV = - P ΔV;  W (-) the system performs a job and the volume increases

.

∴ P = 950 KPa * ( 1000 Pa / KPa ) = 950000 Pa = 950000 J/m³

∴ ΔV = 18 - 5 = 13 L * ( m³ / 1000 L ) = 0.013 m³

⇒ W = - ( 950000 J/m³) * ( 0.013 m³ ) = - 12350 J ( - 12.35 KJ )

⇒ ΔU = 15.6 KJ + ( - 12.35 KJ )

⇒ ΔU = 3.25 KJ