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Chapter 1: 1.2 (page 5)

The Rankine temperature scale(abbreviated °R) uses the same scale size degrees as Fahrenheit, but measured up from absolute zero like Kelvin(so Rankine is to Fahrenheit as Kelvin is to Celsius). Find the conversion formula between Rankine and Fahrenheit and also between Rankine and Kelvin. What is the room temperature on the Rankine scale?

Short Answer

Expert verified

R = 95K and R = 536.67°R

Step by step solution

01

Writing the conversion equations of Kelvin to Celsius and Rankine to Fahrenheit.

The conversion equation for Kelvin to Celsius is,

K = C + 273.15 -----------(1)

and similarly conversion equation for Rankine to Fahrenheit is,

R = F + 459.67 -----------(2)

02

Comparison of Kelvin and Rankine scales at absolute zero,

But we know that, F = 95C+32

substituting this in equation (2),

R = 95C+491.67

substituting C from equation (1), we get,

R =95K

03

Standard room temperature in Celsius scale usually refers to 25°C and using the conversion formula to write in Rankine scale.

The room temperature in Kelvin scale will be 25 + 273.15 = 298.15K

Applying the conversion formula of Kelvin to Rankine scale, we get,

R = 95(298.15)

R = 536.67°R

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Most popular questions from this chapter

When spring finally arrives in the mountains, the snow pack may be two meters deep, composed 50%of ice and 50%of air. Direct sunlight provides about 1000watts/m2to earth's surface, but the snow might reflect 90%of this energy. Estimate how many weeks the snow pack should last, if direct solar radiation is the only source of energy.

Make a rough estimate of the thermal conductivity of helium at room temperature. Discuss your result, explaining why it differs from the value for air.

Calculate the rms speed of a nitrogen molecule at a room temperature?

Your 200 g cup of tea is boiling-hot. About how much ice should you add to bring it down to a comfortable sipping temperature of 65°C? (Assume that the ice is initially 65°C. The specific heat capacity of ice isrole="math" localid="1650146844935" 0.5cal/g°C.

Even at low density, real gases don’t quite obey the ideal gas law. A systematic way to account for deviations from ideal behavior is the virial

expansion,

PV−nRT(1+B(T)(V/n)+C(T)(V/n)2+⋯)

where the functions B(T), C(T), and so on are called the virial coefficients. When the density of the gas is fairly low, so that the volume per mole is large, each term in the series is much smaller than the one before. In many situations, it’s sufficient to omit the third term and concentrate on the second, whose coefficient B(T)is called the second virial coefficient (the first coefficient is 1). Here are some measured values of the second virial coefficient for nitrogen (N2):

T(K)
B(cm3/mol)
100–160
200–35
300–4.2
4009.0
50016.9
60021.3
  1. For each temperature in the table, compute the second term in the virial equation, B(T)/(V/n), for nitrogen at atmospheric pressure. Discuss the validity of the ideal gas law under these conditions.
  2. Think about the forces between molecules, and explain why we might expect B(T)to be negative at low temperatures but positive at high temperatures.
  3. Any proposed relation between P, V, andT, like the ideal gas law or the virial equation, is called an equation of state. Another famous equation of state, which is qualitatively accurate even for dense fluids, is the van der Waals equation,
    (P+an2V2)(V−nb)=nRT
    where a and b are constants that depend on the type of gas. Calculate the second and third virial coefficients (Band C) for a gas obeying the van der Waals equation, in terms of aand b. (Hint: The binomial expansion says that (1+x)p≈1+px+12p(p−1)x2, provided that |px|≪1. Apply this approximation to the quantity [1−(nb/V)]−1.)
  4. Plot a graph of the van der Waals prediction for B(T), choosing aand bso as to approximately match the data given above for nitrogen. Discuss the accuracy of the van der Waals equation over this range of conditions. (The van der Waals equation is discussed much further in Section 5.3.)
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