library(ggplot2)

# Create a data frame with temperature of the cold reservoir values from 260 to 290
df <- data.frame(Tc = seq(260, 300))

# Calculate the corresponding Carnot COP values for a refrigeration system with a hot reservoir temperature of 308K
df$COP1 <- 308 / (308 - df$Tc)

# Scale the COP values by multiplying by 0.4
df$COP1 <- df$COP1 * 0.4

# Calculate the corresponding Carnot COP values for a refrigeration system with a hot reservoir temperature of 328K
df$COP2 <- 328 / (328 - df$Tc)

# Scale the COP values by multiplying by 0.4
df$COP2 <- df$COP2 * 0.4

# Create a line plot of the data
p <- ggplot(df, aes(x = Tc)) +
  geom_line(aes(y = COP1), color = "steelblue") +
  geom_line(aes(y = COP2), color = "red") +
  theme(plot.margin = unit(c(0, 0, 0, 0), "cm")) +
  scale_y_continuous(limits = c(0,10), breaks=seq(0,10,by=1))+
  scale_x_continuous(labels = function(x) round(x - 273, 1), breaks=seq(260,300, by=2))+
  labs(x = "Temperature of Cold Reservoir (K)", y = "Carnot COP",
       title = "Carnot COP for a Refrigeration System with Hot Reservoir Temperature of 308K and 328K")

# Save the plot as a PDF file named "cop.pdf"
ggsave("cop.pdf", plot = p, width = 6, height = 4)