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Lecture 2 Practice: Heat and Enthalpy in Biopharmaceutical Processes

Nine short problems in different formats, of the kinds you may meet in the assessment: sorting, true or false, choosing an equation, reading a graph, finding a mistake, looking up data, a heat balance, working backwards and a multi-step calculation. They start with the ideas and build up to the calculations, so if this topic is new to you, begin with Problem 1. Each answer is checked as you go, and the working is shown once each step is correct.

Equation sheet
  • q = m × C × ΔT  (C in J g−1 K−1: m in g, q in J)
  • Energy = power × time;  1 W = 1 J s−1
  • Mixing: heat gained by the cold liquid = heat lost by the hot liquid
  • n = m / M
  • ΔrH° = ΣnΔfH°(products) − ΣmΔfH°(reactants)
  • Change of state: q = n × ΔvapH (per mole) or q = m × latent heat (per gram)
  • ΔH < 0: exothermic (heat released);  ΔH > 0: endothermic (heat absorbed)
  • A change of 1 °C = a change of 1 K;  1 kJ = 1,000 J;  1 h = 3,600 s
Key terms, if this is new to you
System and surroundings
The system is what we are studying (a dissolving salt, a batch of medium). The surroundings are everything else.
Heat and temperature
Heat, q, is energy transferred because of a temperature difference. Temperature measures how hot something is.
Specific heat capacity, C
The heat needed to warm 1 g of a substance by 1 K. Water's is high: 4.18 J g−1 K−1.
Enthalpy change, ΔH
The heat taken in or given out by a process at constant pressure. Negative: heat out (exothermic). Positive: heat in (endothermic).
Latent heat and ΔvapH
The heat needed to change state (melt, boil, sublime) without any change in temperature.
Standard enthalpy of formation, ΔfH°
ΔH for making one mole of a substance from its elements. Elements such as O2(g) have ΔfH° = 0.

About the values

  • Enthalpies of formation are standard values from the CRC Handbook at 298.15 K and 1 bar.
  • Culture media, buffers and dilute solutions are treated as water: density 1.00 kg L−1 and C = 4.18 J g−1 K−1.
  • No heat is lost to the surroundings unless a problem says otherwise.
  • Small rounding differences are accepted, so you do not need to match every decimal place.
  • Your answers are saved in this browser, so you can leave and come back later.